Dimensionality Reduction, Classification, and Spectral Mixture Analysis using Nonnegative Underapproximation

Nonnegative Matrix Factorization (NMF) and its variants have recently been successfully used as dimensionality reduction techniques for identification of the materials present in hyperspectral images. In this paper, we present a new variant of NMF called Nonnegative Matrix Underapproximation (NMU): it is based on the introduction of underapproximation constraints which enables one to extract features in a recursive way, like PCA, but preserving nonnegativity. Moreover, we explain why these additional constraints make NMU particularly well-suited to achieve a parts-based and sparse representation of the data, enabling it to recover the constitutive elements in hyperspectral data. We experimentally show the efficiency of this new strategy on hyperspectral images associated with space object material identification, and on HYDICE and related remote sensing images.